https://blog.cryptographyengineering.com/2014/11/27/zero-kno... was a good intro for interactive ZK proofs but I haven't been able to find something for non-interactive ones.
This blog post comparing ZK-STARKs to erasure coding is in the right flavor but didn't quite stick to my brain either: https://vitalik.eth.limo/general/2017/11/09/starks_part_1.ht...
A simple signature scheme is based on proof of knowledge PoK{x : pk = g^x}, which is transformed into a noninteractive variant via the Fiat-Shamir transformation, where the message is appended to the hash. Range proofs work similarly, with the simplest form being for a single bit: PoK{(b,r) : C = g^b * h^r & b(b−1)=0}. This proves that commitment C contains a bit b in {0,1} without revealing which value it is.
Arbitrary ranges can then be constructed using the homomorphic properties of commitments. For an n-bit range, this requires n individual bit proofs. Bulletproofs optimize this to O(log n) proof size, enabling practical applications.
The commitment C can be issued by a trusted third party that signs it, and the user can then prove certain properties to a service provider, such as age ranges or location zones (constructed from latitude and longitude bounds).
A key challenge is that reusing the same commitment C creates a tracking identifier, potentially compromising user privacy.
by providing a picture of waldo in the cut-out, you can prove you know where he is without providing the location. a zero knowledge proof.
That doesn't explain the way this scheme works, but it's a nice start.
https://blog.cryptographyengineering.com/2014/11/27/zero-kno...
The non-interactive piece is pretty straightforward you just simulate challenge response conversation with unbiasible public randomness and show the transcript (Fiat Shamir transform).
Another area worth exploring is how some of these proof systems can have such incredibly small proofs (192 bytes for any computation in groth16 zk snarks). That relies on the much more difficult to intuit theory of elliptic curve pairing functions.
For example, in the usecase of providing a proof-of-age to a website: who provides the verification data (the government?); what form does that take (a file in a standard format?); who holds/owns the verification data (the user?); who runs the verification software (the end-user's web browser?).
Can the user use any implementation to provide the proof, or must it be a "blessed" implementation such as Google Wallet?
(2) One of the goals of this project was to layer ZK on top of current identity standards that DMVs already issue, so that gov orgs don't have to change what they currently do to support the strongest user privacy. One example format is called Mdoc.
(3) The user holds the identity information on their device only. No other copies. The user's device makes the zkp proof on-device. This was one of the major technical challenges.
(4) The relying party (eg a website) runs the zk verification algorithm on the proof that is produced by the device to ensure soundness.
(5) Yes, the user can use any compatible implementation to produce the proof. We have open-sourced our implementation and we have a spec for the proof format that others can also reimplement.
The form are eg things like the JSON Web Token (JWT), Digital Credentials, and the Federated Credential Management API (FedCM).[1][2][3][4][5] The software can be anything since they're expected to use open protocols, so yes, web browsers.[6] Per the Commission, "For remote presentation flows, … the Wallet Instance implements the OpenID for Verifiable Presentation protocol OpenID4VP in combination with the W3C Digital Credentials API."[7]
[1] https://en.wikipedia.org/wiki/JSON_Web_Token
[2] https://github.com/w3c-fedid/digital-credentials
[3] https://w3c-fedid.github.io/digital-credentials/
[4] https://github.com/w3c-fedid/FedCM
[5] https://w3c-fedid.github.io/FedCM/
[6] https://github.com/w3c-fedid/FedCM/blob/main/explorations/HO...
[7] https://eu-digital-identity-wallet.github.io/eudi-doc-archit...
Virtually everyone gets their internet from an ISP that is regulated in the country that the user lives in. There are no technical barriers to implementing a permitting system in the United States.
Linking connections to real people is self-enforcing when there is a usage-based tax.
[1] https://www.africanews.com/2018/04/13/uganda-s-social-media-...
I don't like this but don't have another solution other than the porn industry self-policing which isn't promising.
Somehow we've inappropriately shifted responsibility away from parents/guardians in some areas like internet access.
In other areas, like letting your kid go outside by themselves, we've criminalized reasonable caregiver actions.
It's a wild world.
I really like Andy Birrells "micro-cents" which exploited the fact you could not easily reverse an MD5 hash so you one could cheaply do high confidence low value transactions at speed. Another idea that never got anywhere sadly.
ZKP ID cards and ZKP currency are both interesting things from the 90's I'd love to see in real life. Imagine I could pay you phone to phone with no network level of capability using a currency that couldn't be double spent. That was the promise of digicash. The government hated it :-). It was just like cash currency in that serial numbers could let you track the bank it left, and the bank it came back in to, but you couldn't track anywhere it had been between those two points.
Fun times. I'll have to see if some of my ZKP ideas can be built on top of this tech now.
Do you still feel that way knowing that it introduces a hard requirement for all users to have their private data managed by one of Apple, Google, or Microsoft[1]? I want to be excited about this, and about Passkeys, but the people working in this space keep fumbling this ball :(
[1] "Using the MDOC requires a signature from a hardware security key in the phone" https://news.ycombinator.com/item?id=44458417
If only the recipient doesn’t have access, a certain amount of trust can be delegated to the strength of the proof presented in the spend. In an ecash model, the proof would be in the form of a signature made by the mint (assuming the recipient was able to get the public keys the mint was using).
Active research is being done on the ecash model with the resurgence of the concept in the Cashu and Fedimint projects. Cashu takes the online sender, offline receiver approach[2].
[1] https://chaum.com/wp-content/uploads/2021/12/Untraceable_Ele...
^See paragraph in the introduction ending with:
“But if Alice reuses a coin, the bank can trace it to her account and can prove that she has used it twice.”
- Buys or borrows a laptop / phone / whatever from somebody with an authorized private key
- Downloads an authorized private key file from a sketchy forum (maybe hacked from an unwilling target, maybe willingly shared by a free-speech advocate)
- Uses a VPN over HTTPS to visit websites in countries where age checks aren't legally mandated (and non-compliance is implicitly or explicitly encouraged for economic or ideological reasons)
Just like with passkeys or MFA, the "something else" could be purely software though, right? And hence automated?
For example I can run Windows 11 in a virtual machine on Linux, using softu2f to emulate TPM 2.0, and Windows does not know the difference.
In the future, you'll need a signed certificate with your PII/KYC to access the internet and get an IP address. China is already on the way there and the west is warming up to this approach.
The reason I ask is that I know that many teams working in the b-word field are _regularly_ making great progress. So I'm just wondering if this work is actually novel / useful or whether it's Google releasing something that is already stale.
I'll just say that the b-systems solve a different problem, and for the problem solved by our system there is currently no other solution available.
We spoke with Ying Tong and her colleagues from the Ethereum foundation. They have a project investigating which ZK technology would be best for digital credentials, and they have ran a few benchmarks at https://hackmd.io/@clientsideproving/zkIDBenchmarks For reference, our implementation runs the benchmark in about 200ms on the same hardware. The ETHF folks have had access to our code for a while and they agree with this result, but they decided not to publish numbers until the Google code was open-sourced for all. Our system is thus about 10x faster than the closest contender for this problem.
I don't want to make any general claims about who is better than whom. Our system is designed for our problem, and it's not a surprise that another system designed for another problem would perform worse on our problem. We are big fans of the Binius system of Diamond and Posen at Irreducible, and there is a chance that Binius may eventually work better than our stuff. That's however not the case today.
You also have to be careful about which hardware to use. Our implementation is single-threaded no GPU because it has to run on all phones everywhere in the world. Whether or not one can do better on a high-end GPU is irrelevant to us.
Either way, "stale" is not a word I would use. The word I would use is "works today".
It's also an unfathomably complex solution [1] which only a few people in the world will grok, and far more complex than existing solutions such as Idemix or BBS+, which lack such a hardware binding on existing hardware.
Age verification in a privacy preserving way is a really hot topic at the moment, but it will always be possible to bypass it – as will any commonly held anonymous boolean – in quite trivial ways. For example by setting up an open proxy to disclose genuine attributes. There are some privacy preserving mitigations, for example cryptography that'll make you linkable when disclosing more than k times per time period, or detecting slower-than-near-light-speed disclosure in a face-to-face disclosure scenario.
However, these mitigations will never be completely secure. That might not be a problem if it's admitted beforehand so expectations are correctly set: it's a barrier to protect the naïve, not an impenetrable fortress. However, if the expectations are that only age verification that cannot be bypassed is "adequate", we only have to wait for the first incidents in production apps after which the open source and privacy story will be abandoned in the name of security.
[1] https://eprint.iacr.org/2024/2010.pdf and https://eprint.iacr.org/2022/1608.pdf
You can read the docs and whitepaper here: https://docs.reclaimprotocol.org/ And also take a look at all usecases built on top of this tech: https://reclaimprotocol.org/ecosystem
The providers are clutching their OLAP like pearls! :-)
Current benchmarks for proving costs are 33k txns per dollar and we expect this to go down x10-x100 over the coming months/years.
A system that can be trusted needs to work in the real world, with credit card payments, bank accounts, VAT.
But how does it prove that the request is actually made by a person and not a bot? Surely that part is technically impossible right now?
How does the government guarantee that the natural person is such? Various jurisdictions will decide what's good enough, but as a strawman proposal, you go in person to city hall once and upload a document to your phone.
I know someone in germany that got detected cancer in an MRI scanner. The doctor gave him the images and told him to drive to a specialized hospital ~400km away. Otherwise they would send it there with a physical mail and the treatment would have started a week later.
The Sparkasse network is not very well known outside of Germany but is actually Europe's largest financial services group by assets.
What is interesting is that until the 90s the membership banks were public institutions backed by municipal and state guarantees that made them virtually bankruptcy-proof, unlike private banks. EU competition rules then forced Germany to phase out these state guarantees, making Sparkassen subject to normal banking regulations and deposit insurance like other banks.
Our team is leveraging zkVMs for paygo.wtf
